Late to answering this, but here's a stab at it. The question that's easier to ask is why did the steam revolution happen in England when it did as opposed to why didn't it happen elsewhere, but the former can shed light on the latter. In short, there were two major issues in 18th century England that came together. One was that (for various reasons) their domestic labor supply was very expensive. It cost much more to employ an Englishman than it did, say, a Frenchman or someone in China or India. This is largely just a population issue; smaller population means higher demand for labor. The other is that England had largely exhausted its limited burnable forest resources (making ships), leaving it without a cheap source of combustibles for things like heating homes.

The first of these factors led to a push towards automation and labor saving in general, notably in textiles. The second of these factors was the direct push for the steam engine, which was initially used primarily for pumping water out of coal mines (because the surface deposits were relatively quickly exhausted). These two separate innovations came together in a powerful way by the late 18th and early 19th century, in what we think of as the industrial revolution.

So why didn't the Greeks do this? Well, let's look at these two issues in this light. The Greeks had a cheap labor supply, because they engaged in a lot of slavery. They also had considerable natural resources at their disposal and a fairly robust trading network with the other Mediterranean cultures. So there's a) no reason to push for automation, and b) no real reason to push for extensive development of things like a steam engine. They did develop some rather amazing creations that relied on pneumatics, but they were primarily for amusement and a display of knowledge and wealth — complex fountains and the like.

(One can also apply such a question to places like China, as well, where the knowledge prerequisite was also met. The economic answer seems to work out — in places where cheap labor is abundant, there is little drive for automation or mechanization. To get more topical, it is not surprising that places like the United States and Europe, where labor costs are orders of magnitude above the costs of the developing world, are on the forefront of automation technologies today.)

This view of history is slightly Marxist in its approach, but it gives better answers than any other for this sort of thing — the technologies of labor emerged only when the conditions are right for them. Developing steam technology, or automation, was neither cheap nor easy (even in England both took a solid century to perfect). The English needed a very strong motivation to do it, and to provide the financing for its implementation, and for actually taking on the risk of failure. The Greeks in general didn't need to do that sort of stuff, because their economic situation didn't compel them to do it.

(Caveats: big generalizations always smooth over lots of complications, contingencies, etc. As a general outline, this is not a bad place to start in thinking about it. I am not an economic historian; this is just what I've gleaned from reading various economic historians.)